An air puck of mass m1 is tied to a string and allowed to revolve in a circle of

Question

An air puck of mass m1 is tied to a string and allowed to revolve in a circle of radius R on a horizontal, frictionless table. The other end of the string passes through a small hole in the center of the table, and an object of mass m2 is tied to it (see figure below). The suspended object remains in equilibrium while the puck on the tabletop revolves.

(a) Find a symbolic expression for the tension T in the string in terms of m2 and g.
T =
T = m2g ......1
(b) Write Newton's second law for the air puck, using the variables m1, v, and R.
T =

(c) Eliminate the tension T from the expressions found in parts (a) and (b) and find an expression for the speed of the puck in terms ofm1, m2, g, and R.
v =

Explanation / Answer

Given Mass revolving in a circle is m1 Radius of circle is R Mass tied to the other end of the string is m2 a) Tension in the string is           T = m2 g b) Net force acting on m1 is ,      T = m1 v^2 / R c) From parts 1 and 2 , we get     m2 g = m1 v^2 / R        v2 = m2 g R / m1        v = m2 g R / m1 The speed of the puck is m2 g R / m1

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